The refusal came two days after
Sources say the board of directors offer is an indicator that Rupert Murdoch is keen to line up the immediate members of his family to one day take over his reigns of the company.
Elisabeth would have joined her father and brothers Lachlan and James on the board of directors had she accepted.
James, who oversees News International and BSkyB is thought to be his father's likely successor.
Elisabeth founded television production company in 2001. The company supplies content to the BBC, ITV, C4, Five and Sky, including programmes such as 'Gladiators', 'Masterchef', 'Merlin' and 'The Biggest Loser'.
If Murdoch joined the News Corp board, Shine would be ineligible to the 25% budget funding British broadcasters are required to provide to independent production houses -- a key source of revenue for Shine.
The board of directors' role would have also meant that she would have had to quit her position at Shine, in which she owns a 63% stake, or sell the company to News Corp.
News Corp's board currently seats 16 members, and analysts say the company could carry forward the decision not to fill the vacant seat after Elisabeth's refusal.
Chernin, the longtime president and chief operating officer of News Corp and chief executive of Fox Entertainment Group, announced he would not be renewing his five-year contract with the company when it expires in June.
He is expected to run his own film production business once he departs News Corp, but will retain some ties with his former firm.
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